In the first of three 50-minute group matches in the eight-team tournament for Under-19s, the lads found themselves 0-3 down after only sixteen minutes.
Nabil Bentalab pulled a goal back from the penalty spot after good work from Ryan Fredericks soon after half-time, only for Alex Inglethorpe's team to go 4-1 down just two minutes later.
Grant Ward scored late on after superb hold-up play from Victor Zapata-Caicedo to raise hopes of a comeback, but it wasn't to be.
"We started off really brightly and had a good chance to score in the first couple of minutes, and then slightly against the run of play Grasshopper Zurich scored a really good counter-attacking goal," Inglethorpe said after the match.
"From then on, we were the architects of our own downfall because we chased the game a little bit early. We were too gung-ho too soon, and before we knew it, we were 3-0 down at half-time.
"I thought we played a good game in the second half, we were a little bit more considered in what we did, and I saw lots of intensity. Although we came out on the wrong end of it, I thought Ryan Fredericks was exceptional, Alex Pritchard came into it really well and there are certainly some positives to take from the match.
"I thought it was a very good game of youth football in the end."
We face Germany's Hannover 96 and RDC Mallorca of Spain in our remaining group stage matches on Saturday.
Spurs team: Miles, Waller-Lassen, Ball (Z-Caicedo 28), Stewart, Barthram, A.McQueen, Bentaleb, Munns, Fredericks (Ward 35), McEvoy, Pritchard (Lameiras 46)
Goals For: Bentaleb 31, Ward 46
Goals Against: 5, 14, 16, 33